Arrhenius plot

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In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, ( ln ⁡ ( k ) {\displaystyle \ln(k)} , ordinate axis) plotted against reciprocal of the temperature ( 1 / T {\displaystyle 1/T} , abscissa). Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined. The Arrhenius equation can be given in the form: k = A exp ⁡ ( − E a R T ) = A exp ⁡ ( − E a ′ k B T ) {\displaystyle k=A\exp \left({\frac {-E_{\text{a}}}{RT}}\right)=A\exp \left({\frac {-E_{\text{a}}'}{k_{\text{B}}T}}\right)} where: k {\displaystyle k} = rate constant A {\displaystyle A} = pre-exponential factor E a {\displaystyle E_{\text{a}}} = (molar) activation energy R {\displaystyle R} = gas constant, ( R = k B N A {\displaystyle R=k_{\text{B}}N_{\text{A}}} , where N A {\displaystyle N_{\text{A}}} is the Avogadro constant). E a ′ {\displaystyle E_{\text{a}}'} = activation energy (for a single reaction event) k B {\displaystyle k_{\text{B}}} = Boltzmann constant T {\displaystyle T} = absolute temperature The only difference between the two forms of the expression is the quantity used for the activation energy: the former would have the unit joule/mole, which is common in chemistry, while the latter would have the unit joule and would be for one molecular reaction event, which is common in physics. The different units are accounted for in using either the gas constant R {\displaystyle R} or the Boltzmann constant k B {\displaystyle k_{\text{B}}} . Taking the natural logarithm of the former equation gives: ln ⁡ ( k ) = ln ⁡ ( A ) − E a R ( 1 T ) {\displaystyle \ln(k)=\ln(A)-{\frac...